US10979117B2 - Method, system and apparatus for beam forming in a radio frequency transceiver with reduced complexity - Google Patents
Method, system and apparatus for beam forming in a radio frequency transceiver with reduced complexity Download PDFInfo
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- US10979117B2 US10979117B2 US16/540,416 US201916540416A US10979117B2 US 10979117 B2 US10979117 B2 US 10979117B2 US 201916540416 A US201916540416 A US 201916540416A US 10979117 B2 US10979117 B2 US 10979117B2
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01Q—ANTENNAS, i.e. RADIO AERIALS
- H01Q3/00—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system
- H01Q3/26—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system varying the relative phase or relative amplitude of energisation between two or more active radiating elements; varying the distribution of energy across a radiating aperture
- H01Q3/30—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system varying the relative phase or relative amplitude of energisation between two or more active radiating elements; varying the distribution of energy across a radiating aperture varying the relative phase between the radiating elements of an array
- H01Q3/34—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system varying the relative phase or relative amplitude of energisation between two or more active radiating elements; varying the distribution of energy across a radiating aperture varying the relative phase between the radiating elements of an array by electrical means
- H01Q3/42—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system varying the relative phase or relative amplitude of energisation between two or more active radiating elements; varying the distribution of energy across a radiating aperture varying the relative phase between the radiating elements of an array by electrical means using frequency-mixing
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
- H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
- H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
- H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01Q—ANTENNAS, i.e. RADIO AERIALS
- H01Q21/00—Antenna arrays or systems
- H01Q21/24—Combinations of antenna units polarised in different directions for transmitting or receiving circularly and elliptically polarised waves or waves linearly polarised in any direction
-
- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01Q—ANTENNAS, i.e. RADIO AERIALS
- H01Q3/00—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system
- H01Q3/26—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system varying the relative phase or relative amplitude of energisation between two or more active radiating elements; varying the distribution of energy across a radiating aperture
- H01Q3/30—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system varying the relative phase or relative amplitude of energisation between two or more active radiating elements; varying the distribution of energy across a radiating aperture varying the relative phase between the radiating elements of an array
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
- H04B1/38—Transceivers, i.e. devices in which transmitter and receiver form a structural unit and in which at least one part is used for functions of transmitting and receiving
- H04B1/40—Circuits
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
- H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
- H04B7/0842—Weighted combining
- H04B7/086—Weighted combining using weights depending on external parameters, e.g. direction of arrival [DOA], predetermined weights or beamforming
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/10—Polarisation diversity; Directional diversity
Definitions
- Embodiments of the present disclosure relate to wireless transceivers and more particularly relate to method, system and apparatus for beam forming in a radio frequency transceiver with reduced complexity.
- Wireless transceivers often employ RF antennas for radiating and collecting the RF signal (electromagnetic waves) for transmitting and receiving wireless signals.
- wireless communication system such as 3G/4G/5G systems, RADAR systems and object detection systems employ RF antennas to transmit and receive RF signals.
- the antenna radiates the RF signal energy in all directions.
- the energy transmitted in any desired direction is lesser than the total energy/strength radiated by the antenna.
- beam forming techniques are employed. In the beam forming technique multiple phase shifted version of the RF signal are transmitted or received on a plurality of antennas (antenna array) as is well known in the art.
- beam forming (generating multiple phase shifted signals) is performed in analog mode, digital mode and hybrid mode.
- FIG. 1A illustrates an example conventional analog beamforming.
- the antennas 110 A-N receives the RF signals
- the phase shifters 120 A-N shift the phase of the corresponding received RF signals
- the combiner 130 combines the phases sifted RF signals.
- the multiplier 140 and local oscillator (LO) 145 converts the RF signal received from the combiner to base band signal for further processing.
- Xi represents signals received from antennas
- W i represents the weights (phases shift and gain) provided to the corresponding ones of X i signals.
- the W i requires to be in smaller phase values (at least when beams are required to be steered in smaller angle or good angular resolution).
- the analog conventional beam forming places limitation (at least in terms of the analog hardware part) on the smaller phase values in W i .
- FIG. 1B illustrates an example conventional digital beam forming.
- the antennas 110 A-N receives the RF signals
- the mixers 150 A-N mixes the RF signals on corresponding channels 116 A-N with a reference signal from LO 160 to convert each RF signal to respective baseband signals 157 A-N.
- Digital Beam former 170 performs beam forming to provide baseband beams on paths 171 and 172 .
- the conventional digital beam former 170 may perform digitization of the RF signal and may perform matrix multiplication with the weight matrix. Due to digital processing with large bit width multipliers, a smaller beam width (high resolution) may be obtained. In other words, a smaller phase shifts may be achieved in the digital processing, thereby accommodating any desired beam direction and resolution.
- the digital beam former increases the complexity of the hardware as the number of base band converter (base band processing channels) increase with increasing number of receiving/transmitting antennas.
- FIG. 1C illustrates an example conventional hybrid beam forming.
- the antennas 110 A-N receives the RF signals
- the analog beam former 180 generates set of beams 181 A-D
- the Base band processing channel 185 A-D converts the RF beam 181 A- 181 D to corresponding baseband beam 186 A-D
- digital beam former 190 performs digital beam forming on the base band signals 186 A-D to generate digitized beams 191 A-C.
- the number of base band converting channels is reduced due to first level of analog beam forming ( 180 ) and the benefits of smaller phase angles (high resolution) are obtained by employing the digital beam former ( 190 ).
- the conventional hybrid beam former reduces the hardware complexity by reducing the number of baseband processing channels.
- such reduction in the hardware causes the reduced flexibility at the digital beam former.
- a radio frequency receiver for beamforming comprises a plurality of receiving antennas providing a plurality of radio frequency (RF) signals, a first set of phase shifters providing a first set of analog beams from a first set of RF signals in the plurality of RF signals, a second set of phase shifters providing second set of analog beams from a second set of RF signals and a digital beamformer providing final set of beams employing the first set of analog beams and the second set of analog beams.
- the receiver further comprises a set of splitters generating a copy of the first set of RF signals, wherein the second set of RF signals are the copy of the first set of RF signals.
- the receiver further comprises a first set of delay elements adding a first delay in time to each of the first set of analog beams and a second set of delay elements adding a second delay in time to each of the second set of analog beams before providing to the digital beamformer.
- a radio frequency transmitter for beamforming comprises a plurality of transmitting antennas transmitting a set of radio frequency (RF) signals, a digital beamformer providing a plurality of digital beams, a first set of splitter splitting a first set of digital beams in the plurality of digital beams into first set of analog beams, a second set splitter splitting a second set of digital beams in the plurality of digital beams into second set of analog beams, a first set of phase shifters providing a first set of analog beams, a second set of phase shifters providing second set of analog beams, a set of adder adding the first of analog beams and second set of analog beams to form the set of RF signals.
- RF radio frequency
- FIG. 1A illustrates an example conventional analog beam forming.
- FIG. 1B illustrates an example conventional digital beam forming.
- FIG. 1C illustrates an example conventional hybrid beam forming.
- FIG. 2 is an example RF transceiver system in an embodiment.
- FIG. 3 is an example receiver section illustrating the beam forming in an embodiment.
- FIG. 4 is an example receiver section with a differently polarised antenna illustrating the beam forming in an embodiment.
- FIG. 5 is a block diagram illustrating the transmitted section in an embodiment.
- FIG. 2 is an example RF transceiver system in an embodiment.
- the transceiver is shown comprising antenna array 210 , transmitter section 220 , receiver section 230 , signal processor 250 , and input/output (I/O) devices 270 . Each block is further described below.
- the antenna array 210 operates to transmit and receive RF signal over the free space 205 .
- the antenna array 210 may be a one dimensional array or a two dimensional array. In that, elements may operate in a time divisional manner to transmit and/or receive. Alternatively, the dedicated antenna elements may be interspersed in the array pattern.
- the transmitter section 220 provides a set of successively phase shifted version of a RF signal for transmission over the antenna array 210 .
- the phase difference between the successively phase shifted signals of each RF signal causes an RF beam with a gain A and beam width B to be formed in the free space when transmitted over the antenna array 210 .
- the receiver section 230 receives a set of RF signals from the antenna array 210 .
- the receiver 230 determines the beam from the set of received RF signal.
- the beam direction and other information are provided for further processing on the path 235 .
- the signal processor 250 provides a signal to the transmitter 220 for transmission and receives a signal from the receiver 230 for further processing.
- the transmitter 220 , receiver 230 and processor may be implemented as single system on chip (SOC) integrated circuit device. As a result, intercommunication and signal flow between the units may occur as per the architecture of the SOC.
- SOC system on chip
- the I/O devices 270 provide various interface to external world.
- the I/O devices 270 may comprise, display device for controlling and viewing the operation/result.
- the I/O device 270 may comprise input devices like keypads, etc., for receiving the signal and commands for processing.
- the RF transceiver 201 operate as 3G/4G/5G communication system.
- the RF transceiver may operate as RADAR system to determine the object.
- the transmitter 220 and receiver 230 perform beam forming to respectively transmit the RF signal in a desired direction and determine the direction of the received RF signal.
- the manner in which the beam forming is performed in the transmitter and receiver in an embodiment is further described below.
- FIG. 3 is an example receiver section illustrating the beam forming in an embodiment.
- the receiver section is shown comprising antenna array 310 A-N, analog splitters 320 A- 320 N, first set of phase shifters 330 A-N, second set of phase shifters 340 A-N, analog combiner 350 A & B, delay elements 360 A & B, mixer 370 A-K, LO 380 , and digital beam former 390 .
- Each element is described in further detail below.
- the antenna array 310 A-N operate to receive RF signal over the free space.
- the antenna array 310 may be deployed and operative similar to antenna array 210 .
- Each antenna 310 A-N captures electromagnetic RF signal and provides the captured RF signal on the path 312 A-N.
- the splitter 320 A-N splits the RF signal on each path 312 A-N to respective paths of 323 A-N and 324 A-N.
- the splitter may divert/copy/split the signal received from each antenna on to multiple paths.
- the splitter 320 A-N is shown to copy the signal on to only two paths merely for illustration.
- the splitters 320 A-N may be implemented by simply joining the conductor paths.
- splitter may be implemented as an electronic circuitry that provide signal with enhanced strength on the paths without loading the antenna.
- the first set of phase shifters 330 A-N shifts the phase of the signal received on the corresponding paths 323 A-N by corresponding set of values such that they are mutually shifted in phase and amplitude.
- the signal on path 323 A may be shifted by a value ⁇ 1
- the signal on path 323 B may be shifted by a value ⁇ 2 and so on.
- the magnitude and phase changes provided by the phase shifters 330 A-N (in case of a complex multipliers) to the signal on paths 323 A-N may be respectively represented by weights W 1 through W N .
- the signals weighted by the first set of phase shifters 330 A-N is provided respectively on paths 335 A-N.
- the second set of phase shifters 340 A-N shifts the phase of the signal received on the corresponding paths 324 A-N by corresponding set of values.
- the signal on path 324 A may be shifted by a value ⁇ 1
- the signal on path 324 B may be shifted by a value ⁇ 2 and so on.
- the magnitude and phase changes provided by the phase shifters 340 A-N to the signal on paths 324 A-N may be respectively represented by weights U 1 through U N .
- the signals weighted by the second set of phase shifters 340 A-N is provided respectively on paths 345 A-N.
- the analog combiner 350 A combines the signal on paths 335 A-N and the analog combiner 350 B combines the signal on paths 345 A-N.
- the combiner 350 A and 350 B may perform signal summation operation in an embodiment.
- the analog combiner 350 A and 350 B respectively provides the combined signal on path 356 A and 356 B.
- the combined signal on path 356 A and 356 B represents the first level of beam forming as an analog beamforming.
- the x i representing the RF signal from the i-th antenna 310 A-N
- the W i representing weights (phase angle and gain) provided by the first set of phase shifters 330 A-N
- the U i representing weights (phase angle and gain) provided by the second set of phase shifters 340 A-N.
- the delay elements 360 A & 360 B delays the signals on paths 356 A and 356 B.
- the delayed signals are provided on path 367 A & B.
- the delay added to each path may be represented as ⁇ 1 and ⁇ 2 .
- the signal on paths 367 A and 367 B may be represented by relation y 1 (t 1 ⁇ 1 ), y 2 (t 2 ⁇ 2 ) and so on.
- the local oscillators (LO) 380 provides a reference frequency signal to convert the combined RF signals 367 A and 367 B to base band signals.
- the mixer 370 A and 370 B mixes the signal on path 367 A and 367 B with the reference signal from the LO 380 to convert the RF signal on paths 367 A and 367 B to base band signal.
- the base band signal is from the mixer 370 A and 370 B is provided on path 379 A and 379 B to the digital beam former 390 .
- the digital beam former 390 perform digital beam forming using the signal received on the paths 379 A and 379 B.
- the digital beam former 390 may comprise base band signal processing circuitry, analog to digital converters, etc., for each base band signal path 379 A and 379 B.
- k number of beams are formed and provided on paths 399 A-K.
- the digital beams on the paths 399 A-K may be represented as:
- [ z 1 z 2 ⁇ z L ] [ D 11 ... D 1 ⁇ k ⁇ ⁇ ⁇ D L ⁇ ⁇ 1 ... D Lk ] ⁇ H ⁇ [ y 1 ⁇ ( t 1 - ⁇ 1 ) y 2 ⁇ ( t 2 - ⁇ 2 ) ⁇ y k ⁇ ( t k - ⁇ k ) ] ( 4 )
- the z 1 through z L representing digital beams on paths 399 A-K
- D 11 through D Lk digital weights of the digital beam former 390
- D 11 through D kk are arranged in a L ⁇ k matrix.
- the example receiver section 301 is illustrated with the two combiners for illustration.
- the number of combiners may be desirably selected to perform analog beam forming on the RF signal with desired resolution.
- the combiners and the set of antennas coupled to the combiners may be selected by choice to provide variable number of base band channels to the digital beam forming.
- the receiver section 301 provides larger flexibility to select the number of base band channels to digital beam former 390 for digital beam forming.
- the second set of phase shifters, delay elements may enhance the antenna aperture without increasing the number of antennas.
- the delay values may be selected corresponding to antenna array position and the phase values of U n may be set equal to W n for increased antenna aperture.
- the delay element value may be set to zero and the U n may be selected different from W n to increase the number of beams provided to the digital beam former.
- analog splitters 320 A- 320 N, and values of first set of phase shifters 330 A-N, second set of phase shifters 340 A-N, analog combiner 350 A&B and the delay elements 360 A and B may be selectively adjusted to either provide more number of RF beams to the digital beam former and/or may be adjusted to provide increased antenna aperture by concatenating time delayed version of the RF beamformer output.
- the receiver section 301 may be further represented by a relation:
- the weights A 11 through A Ln represents the combined effective weights (with or without the delays Delta_i in each of the paths).
- the delays can be incorporated by multiplying by suitable complex phase in the case of narrow band signals.
- delays are incorporated separately, and they are not part of H matrix obtained from both analog part and digital part of the beamformer.
- the values A 11 through A Ln in the matrix H determines the resolution, direction, strength of the beam formed by the system 301 .
- the matrix H represents the beam former transfer function of 301 . Accordingly, the suitable values for weights A 11 through A Ln may be set to obtain the desired beam performance.
- a 11 through A Ln may be decomposed into analog and digital weights w, U, and D in a suitable manner. For example, more precession sensitive weights may be moved to digital beam former and lesser precession weights may be incorporated in the analog part.
- the manner in which the matrix H may be decomposed in to analog and digital weights is further discussed below.
- the summation operation may be performed within the digital beam former 390 itself.
- the digital beamformer operation may be viewed as product of the weight matrix and the data vector coming from the analog beamformer (after down conversion and ADC). This is automatically done here by the matrix multiplication of V H .
- weights of H may be decomposed as:
- the weights of H may be decomposed using Q and R decomposition (also referred to as QR factorization).
- Q and R decomposition also referred to as QR factorization
- the Q representing digital weights matrix and is a unitary matrix and R representing the analog weights and is an upper triangular matrix with a reduced number of weights.
- the weights of H may be decomposed using S and P decomposition (also referred to as Polar decomposition).
- S and P decomposition also referred to as Polar decomposition
- FIG. 4 is an example receiver section with a differently polarised antenna illustrating the beam forming in an embodiment.
- the receiver section 401 is shown comprising antenna array 410 A-N and 420 A-N, first set of phase shifters 430 A-N, second set of phase shifters 440 A-N, analog combiner 450 A&B, delay elements 460 A and B, mixers 470 A-K, LOs 480 A-K, and digital beam former 490 . Each element is described in further detail below.
- the first set of phase shifters 430 A-N, second set of phase shifters 440 A-N, analog combiner 450 A&B, delay elements 460 A and B, mixers 470 A-K, LOs 480 A-K, and digital beam former 490 respectively operate similar to the elements the first set of phase shifters 330 A-N, second set of phase shifters 340 A-N, analog combiner 350 A&B, delay elements 360 A and B, mixers 370 A-K, LOs 380 A-K, and digital beam former 390 described with reference to the FIG. 3 .
- the antenna array 410 A-N are differently polarised compared to the antenna array 420 A-N.
- antenna array 410 A-N may be vertically polarised while antenna array 420 A-N is horizontally polarised.
- the RF signals from antenna 410 A-N are provided to the first set of phase shifters 430 A-N and the RF signals from the antenna 420 A-N are provided to the second set of phase shifter 440 A- 440 N.
- the antenna array 410 A-N and antenna array 420 A-N are interposed to make a single antenna array pattern.
- the two antenna array may be deployed making separate pattern.
- the half the number of the antenna elements M/2 may be vertically polarised to form the antenna array 410 A-N and another half may be horizontally polarised to form 420 A-N.
- FIG. 5 is a block diagram illustrating the transmitted section in an embodiment.
- the transmitter section 501 is shown comprising digital beam former 510 , local oscillators 530 , mixers 520 A & B, delay elements 540 A & B, analog splitters 550 A & B, first set of phase shifter 560 A-N, second set of phase shifters 570 A-N, adders 580 A-N, and antenna array 590 A-N. Each element is described in further detail below.
- the transmitter section 501 is configured to operate in juxtaposition with the receiver 301 .
- the flow of signal is in reverse direction compared to the receiver section 301 .
- the operations of each element and the signal flow may be apparent to a person skilled in the art by reading the disclosure herein. However, the operation is briefly described for conciseness.
- the digital beam former 510 performs the first level of beam forming from the received signal 505 .
- the signal 505 may be received from processor or I/O devices.
- the digital beam former 510 may comprise digital to analog convertor (DAC) (not shown) to provide a baseband signals with the multiple beams. In one embodiment, the digital beam former provides two base band beams on path 512 A and 512 B.
- DAC digital to analog convertor
- the mixers 520 A&B and the local oscillator 530 together operate to transform the base band signals on path 512 A&B to RF signals by mixing operation.
- the converted RF signals are provided on path 524 A&B.
- the delay elements 540 A&B add delay to the RF signal on path 524 A&B, the delayed RF signal is provided on path 545 A&B.
- Each splitter 550 A and 550 B splits the signal on respective paths 545 A and 545 B into N signals.
- the splitter 550 A provides the split N number of signals on the paths 556 A-N and the splitter 550 B provides the split N number of signals on the paths 557 A-N.
- the first set of phase shifters 560 provides a first set of phase shifts to the signals on the paths 556 A-N.
- the phase shifted RF signal is provided on paths 568 A-N.
- the second set of phase shifters 570 provides a second set of phase shifts to the signals on the paths 557 A-N.
- the phase shifted RF signals are provided on path 578 A-N.
- the adders 580 A-N adds the corresponding phase shifted signals on paths 568 A-N with 578 A-N. The added signals are provided on path 589 A-N.
- the antennas 590 A-N transmits the signal on paths 589 A-N to the free space.
- the digital beam former 510 performs first level of beam forming and the analog splitter, first set of mixers, second set of mixers, and adders, operate to provide second level of beam forming in the digital domain.
- the transmitter section 501 may be implemented in similar manner as receiver section 301 .
- the analog weights and digital weights may be determined using any relation 4, 5, 6.
Abstract
Description
Y=Σ i=0 n W i X i, (1)
In that, Xi represents signals received from antennas, Wi represents the weights (phases shift and gain) provided to the corresponding ones of Xi signals. Accordingly, as the number of antenna increases to reduces the beam width, the Wi requires to be in smaller phase values (at least when beams are required to be steered in smaller angle or good angular resolution). The analog conventional beam forming places limitation (at least in terms of the analog hardware part) on the smaller phase values in Wi.
Y=WX, (2)
in that, W represents a weight matrix and X represents the input baseband signal vector.
y 1=Σi=0 n W i x i ,y 2=Σi=0 n U i x i, so on. (3)
In that, the xi representing the RF signal from the i-
In that, the z1 through zL representing digital beams on
in that, matrix H representing an equivalent weight matrix from both analog part of the beam forming (
In that, the UΣ representing digital weights and is a matrix and VH analog weights and is also a unitary matrix as precision requirements are less for unitary matrices. Further, it may be decided as to which beam should be given more importance (or higher precision) based on the singular value matrix Σ. In accordance with the decomposition, the summation operation (combiner operation) may be performed within the digital beam former 390 itself. The digital beamformer operation may be viewed as product of the weight matrix and the data vector coming from the analog beamformer (after down conversion and ADC). This is automatically done here by the matrix multiplication of VH.
In that, the U representing digital weights and is a unitary matrix and ΣVH analog weights and is scaled unitary matrix with a smaller dimension and less weights.
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